Find the minimum value of the function `f(x) = (pi^(2))/(16 cot^(-1) (-x)) - cot^(-1) x`

Explanation

To find the minimum value of the function \( f(x) = \frac{\pi^2}{16 \cot^{-1}(-x)} - \cot^{-1}(x) \), we will follow a systematic approach.

### Step 1: Rewrite the function
We start with the function:
\[ f(x) = \frac{\pi^2}{16 \cot^{-1}(-x)} - \cot^{-1}(x) \]
Using the property of inverse cotangent, we know that:
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